MOV is QuickTime's container - what iPhones and Macs record. The open secret is that MP4 was standardised *from* it, so the two share their internal structure almost exactly, and reading one is reading the other. Writing a true MOV is another matter, which is why it converts from here but not to.
Every conversion below runs in this page, on your own machine. Nothing is uploaded, there is no queue, and there is no account to make. Pick a target format, or just drop a MOV file above and choose afterwards.